Decentralized Sensor Network Localization using Matrix-Parametrized Proximal Splittings

TL;DR

This work advances decentralized sensor network localization by applying a matrix-parametrized proximal splitting method to the node-based SDP relaxation, while respecting the sensors’ communication graph. It introduces a fully decentralized Sinkhorn-Knopp approach to construct the splitting parameters, enabling scalable, parallel proximal updates under a $2$-Block design. Compared to decentralized ADMM, the proposed method shows faster convergence and lower memory usage, and it often yields location estimates closer to the true positions even before full SDP convergence. A practical early-stopping criterion further enhances accuracy, suggesting the iterates prior to convergence can outperform the relaxation’s optimal solution in many scenarios, with significant implications for real-time decentralized localization.

Abstract

We present a novel application of a recently-proposed matrix-parametrized proximal splitting method to sensor network localization, the problem of estimating the locations of a set of sensors using only noisy pairwise distance information between the sensors. The decentralized computation required by our approach respects the communication structure between sensors specified by the noisy SNL problem, thereby allowing individual sensors to estimate their location using only local computations and communication with their neighbors. Our proposed method experimentally outperforms a competing method for decentralized computation -- the alternating direction method of multipliers (ADMM) -- with respect to convergence rate and memory use. As an independent methodological contribution, we propose using the Sinkhorn-Knopp algorithm in a completely decentralized manner to construct the matrices which parametrize our proposed splitting method. We show that parameters selected using this method perform similarly to those selected via existing parameter selection methods while requiring far less computation. Unlike centralized interior point solution methods, our first order splitting method allows for efficient warm starting, and we demonstrate improvements in convergence using rough estimates of sensor location to warm start our algorithm. We also find that early termination of the algorithm provides more accurate location estimates than the minimizer of the node-based SDP relaxation of the SNL.

Figures (4)

• Figure 1: Relative error from the true location for Algorithm \ref{['n_iteration']} and ADMM
• Figure 2: Matrix design comparison
• Figure 3: Early termination solution centrality
• Figure 4: Early termination performance

Theorems & Definitions (4)

• theorem 1
• proof
• Corollary 1.1
• proof